346 Part 4 Investing in Long-Term Assets: Capital Budgeting
11-5 REINVESTMENT RATE ASSUMPTIONS
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The NPV calculation is based on the assumption that cash in" ows can be rein-
vested at the project’s risk-adjusted WACC, whereas the IRR calculation is based
on the assumption that cash " ows can be reinvested at the IRR. To see why this is
so, consider the following diagram, which was! rst used in Chapter 5 to illustrate
the future value of $100 when the interest rate was 5%.Going from PV to FV: PV = $100.00(^0) 5% (^1) 5% (^2) 5% 3
$105.00 $110.25 $115.76 = FV
Observe that the FV calculation assumes that the interest earned during each year
can be reinvested to earn the same 5% in each succeeding year.
Now recall that when we found the PV, we reversed the process, discounting
rather than compounding at the 5% rate. This diagram was used to demonstrate
this point:
Going from FV to PV: PV = $100.00
(^0) 5% (^1) 5% (^2) 5% 3
$105.00 $110.25 $115.76 = FV
This led to the following conclusion: When we calculate a present value, we are implic-
itly assuming that cash " ows can be reinvested at a speci! ed interest rate, 5% in our exam-
ple. This applies to Projects S and L: When we calculated their NPVs, we discounted
at the WACC, 10%, which means that we were assuming that their cash " ows
could be reinvested at 10%.
Now consider the IRR. In Section 11-3 we presented a cash " ow diagram set
up to show the PVs of the cash " ows when discounted at the IRR. We saw that the
sum of the PVs is equal to the cost at a discount rate of 14.489%; so by de! nition,
14.489% is the IRR. Now we can ask this question: What reinvestment rate is built
into the IRR?
Since discounting at a given rate assumes that cash " ows can be reinvested at that
same rate, the IRR assumes that cash " ows are reinvested at the IRR.
The NPV assumes reinvestment at the WACC, while the IRR assumes reinvest-
ment at the IRR. Which assumption is more reasonable? For most! rms, assuming
reinvestment at the WACC is more reasonable for the following reasons:
- If a! rm has reasonably good access to the capital markets, it can raise all the
capital it needs at the going rate, which in our example is 10%. - Since the! rm can obtain capital at 10%, if it has investment opportunities with
positive NPVs, it should take them on and it can! nance them at a 10% cost. - If the! rm uses internally generated cash " ows from past projects rather than
external capital, this will save it the 10% cost of capital.^ Thus, 10% is the
opportunity cost of the cash " ows, and that is the effective return on reinvested
funds.
To illustrate all this, suppose a project’s IRR is 50%, the! rm’s WACC is 10%, and
the! rm has adequate access to the capital markets. Thus, the! rm can raise all the
capital it needs at the 10% rate. Unless the! rm is a monopoly, the 50% return
would attract competition, which would make it hard to! nd new projects with a(^12) This section gives a theoretical explanation of the key di" erence between NPV and IRR. However, it is relatively
technical; so if time is a constraint, professors may decide to have students skip it and just read the box titled,
“Why NPV Is Better Than IRR,” which appears earlier in the chapter.